Microeconomics
ECON 100A
Problem Set 3 Solutions
Due October 13, 2010 (Solutions Posted October 15, 2010)
1.
Toni’s utility is
3
2
3
)
,
(
z
x
z
x
U
=
a.
Does Toni consider X and Z goods?
(“Goods” are items we like more of, ie. more is better.
“Bads” are items that we like to have less of, ie. less is better. For example, pizza is a good.
Garbage is a bad.) Prove your answer.
b.
What is Toni’s marginal rate of substitution between goods x and z (her MRS)?
c.
Are Toni’s indifference curves convex?
Prove you answer.
2.
Consider the constrained optimization problem. [This question is especially important because it
enables you to solve for consumer demand functions from scratch.]
Y
z
p
x
xz
z
x
U
z
z
x
=
+
=
x
3
,
p
subject to
3
)
,
(
max
a.
List the choice variables.
b.
List the parameters.
c.
Are they goods or bads? Prove this.
d.
Are they convex?
e.
Draw an indifference curve diagram and budget line and show the optimal bundle of
goods for the consumer.
f.
Set up the Lagrangian.
g.
Write down the first order conditions.
h.
Calculate the optimal choice of x and z.
i.
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 Fall '08
 ZAMBRANO
 Microeconomics, Utility, indirect utility function, Z. Toni

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